Even function limits Suppose f is an even function where lim x...

Question

Even function limits Suppose f is an even function where lim x→1^− f(x)=5 and lim x→1^+ f(x)=6. Find lim x→−1^− f(x) and limx→−1^+ f(x).

Accepted Answer

Hello there today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Consider G is an even function where the limit as X approaches two to the two from the left G of X equals seven and limit X approaches two from the right G of X is equal to eight. Evaluate the limits given below the limit evaluated at X approaches negative two from the right G of X and the limit as X approaches negative two from the left G of X. Awesome. So it appears for this particular problem we're asked to ultimately evaluate the limits, which is the limit once again as X approaches negative two from the right of GG FX and the limit as X approaches negative two from the right of G FX Awesome. So now that we know that we're trying to evaluate these specific limits, let us read, offer multiple choice sensors to see what our final answer pair might be noting that our first answer is for the limit as X approaches negative two from the left of G of X. And our second answer is for the limit as X approaches negative to, from the right G of X and they're all equal to sum number. So A is seven and eight, B is eight and eight, C is seven and seven and D is eight and seven. Awesome. So to, in order to solve this problem, we must first note, we need to recall a note that since G is an even function, we will be able to write easily that G of X is equal to G of negative X for all X Awesome. And we can also go ahead and easily write, as we should recall a note that for the limit as X approaches negative two from the left is that's what that negative power means that negative sign in the power means that it's going to be evaluated from the left. That's what the negative sign means. So the limit as X approaches negative two from the left of G of X fantastic, we can consider the limit as X approaches negative to from the left. And as we should recall a note that since G is even this will be equivalent to the limit as X approaches two from the right G of X Awesome. So on moving right along here, so therefore, without a doubt, we can go ahead and write that the limit. And this is the limit as X approaches negative two from the left of G FX will be equal to the limit as X approaches two from the right of G FX, which is all equal to eight. So without a doubt, we can recall and note that for the limit. Uh so this is the limit where X approaches negative two from the right of G of X Awesome, we can consider the limit as X approaches negative two from the right because that positive sign in the power means that it's gonna be approaching from the right. So since G is even this will mean that it's equivalent to the limit as X approaches to from the left of G of X. So therefore, without a doubt, that will mean that we can go ahead and write that the limit as X approaches negative two from the right of G of X will be equal to the limit as X approaches two from the left G FX will be equal to seven. So without a doubt, our final answer has to be looking at our multiple choice answers, multiple choice answer letter D which states once again that the limit which is X approaches negative two from the left of G of X equals eight. And the limit as X approaches negative two from the right of G of X is equal to seven and that is it. Thank you so much for watching. Hopefully, that helped and I can't wait to see you in the next video. Bye.

Even function limits Suppose f is an even function where lim x→1^− f(x)=5 and lim x→1^+ f(x)=6. Find lim x→−1^− f(x) and limx→−1^+ f(x).

Key Concepts

Even Functions

Limits from the Left and Right

Limit Properties of Even Functions

Watch next